In IC design, minimum width and minimum distance of shapes are the most fundamental design rules in the generation of lithographic masks for IC manufacturing. When applied to polygons, these design rule checks are widely available in a variety of Electronic Design Automation tools for design and verification of IC, IC packages and printed circuit boards. For certain applications, however, the use of more general classes of shapes than polygons is required. For example, the shapes of silicon photonics, MEMS and microfluidics devices may be the result of the mathematical solution of some underlying physical model and therefore most naturally described by curves given by arbitrary parametric functions. For these applications, the existing methods for checking minimum width and minimum distance of polygons are no longer sufficient and need to be extended to more general shapes whose boundaries consist of arbitrary curves. However, checking of minimum width and minimum spacing on polygons that are approximation of curved boundaries can lead to false violations or even miss some violations entirely. In addition, for arbitrary curves the checking of maximum curvature is also required, which is not provided by current tools for checking polygons.
It is desirable to provide a method and a strategy for checking the minimum width and the minimum distance of planar region boundaries defined by arbitrary parametric curves, while also checking the maximum positive (convex) curvature and the minimum negative (concave) curvature, respectively, of the boundary curves.
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